A writer's livelihood depends on their ability to analyze the available markets and find work for themselves. With the advent of the internet there seem to be more opportunities opening for writers daily. Taking advantage of the market is about research, patience, confidence and persistence.
The single largest key to breaking into the market is spending time doing research. There are more available magazines and newspapers out there than most writers might think. Search the internet and you may turn up the perfect place to pitch to.
There are many books out there on the business aspects of freelancing that could be of service. One of my favorites is "Make a REAL LIVING as a Freelance Writer" by Jenna Glatzer. Glatzer is a well known author of books and magazine pieces, and covers subjects from pitching to interviews to invoicing.
Even small, local public libraries tend to have a few back issues of a variety of magazines. Take the time to study publications that you are considering pitching. Study the tone and length of the articles and think about where your idea might fit best. If possible, get a copy of the magazine's editorial calendar. This will let you know what the themes and topics of future editions will be, so you can send appropriate ideas.
The process can be time consuming. Editors are often notoriously slow to respond to queries. Do not expect an immediate response to your email or letter, although they do happen sometimes. Editors are busy people and reviewing pitches is a low priority.
After a month has passed, if you haven't received any response to your email or letter, it is appropriate to follow up and make sure that the editor received your query. Make sure you are professional in all future contacts and "nudging."
Many writers limit the growth of their career because of self-doubt. If you have a proposal for an article that would be perfect for a major, national magazine then find the appropriate editor and send it!
Also, have confidence when it comes to your pay rates. Too many writers continue to write for free or very low pay when they have the opportunity to move on. If you have previously written for a magazine and have proven that you do good work and get it in before the deadline, then try asking for a slightly higher rate. There are freelance writers out there making more than $1 per word - wouldn't you like to be among them?
Inevitably, writers will face rejection. No matter how talented you may be your style will not be the right fit for every magazine or website that you query. This does not mean that your idea isn't worthy. Continue to pitch other magazines! If you believe that your story is good, there will be someone out there who wants it. Develop a tough skin and be tenacious.
Spend time learning as much as you can about the market, and you will be rewarded. Good luck and happy writing!